a(n)=a(n-1)+a(n-2)-d, where d=a(n/4) if 4 divides n, else d=0; 2 initial terms.

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =4a(5) =6a(6) =10a(7) =15a(8) =25a(9) =40a(10) =65a(11) =103a(12) =168a(13) =271a(14) =439a(15) =708a(16) =1147a(17) =1855a(18) =3002a(19) =4853a(20) =7855a(21) =12708a(22) =20563a(23) =33265a(24) =53828a(25) =87093a(26) =140921a(27) =228004a(28) =368925a(29) =596929